# How do I interpret a loss of significance when adding another term to a model? [duplicate]

I have several regressions in my bachelor's thesis about macro economics. In the first regression one particular coefficient was significant on the 5% level. Let's call the significant coefficient C1, with ic being the intercept.

$$Y_t = ic_t + βC1_1 + ε_t$$ This significance went away as I added another term with a dummy variable in front of the same variable. $d$ is the dummy variable, and it is only equal to $1$ in $15$% of the observations.

$$Y_t = ic_t + βC1_t + θd_t*C1_t + ε_t$$

How do I interpret that? I thought it should be interpreted as a type I error, but my supervisor said that it shouldn't be interpreted that way, and also said I shouldn't be talking about type I/II errors, without any further explanations as to why not. I had no opportunity to ask why not either.

So how is this loss of significance supposed to be interpreted?

Edit: I was referred to another topic below, however that topic deals with introducing a completely new variable. In my case I don't see how the interpretation can still be that "holding this constant..." etc, as I am introducing a term that is essentially the same variable just in different circumstances, when d is equal to 1.

Edit2: Again, the second topic I have been referred to and had this topic marked as identical to, does not answer this question.

• It is not a good idea to include an interaction without also including all the main effects (here you have left out $d$) unless you are sure you know what that model means. – mdewey Jan 3 '18 at 13:34
• Do you mean that I left out d in the first regression? – Chisq Jan 3 '18 at 14:07